1. Symmetry Viviana C. Castellón East Los Angeles College MEnTe Mathematics Enrichment through Technology

2. Symmetric with Respect to the x-Axis A graph that is symmetric to the x-axis, can be seen as slicing a figure horizontally. In other words, for every point (x,y) on the graph, the point (x,-y) is also on the graph.

3. The figure illustrates symmetric with respect to the x-axis. The part of the graph above the x-axis is a reflection (mirror image) of the part below the x-axis.

4. The following figures illustrate symmetric with respect to the x-axis

5. Testing for Symmetry with respect to the x-axis Substitute -y for every y in the equation. If the equation is EXACTLY as the original equation, the graph is symmetric with respect to the x-axis.

6. Testing for Symmetry with respect to the x-axis The following equation is given: Substitute –y for every y. Since the equation is EXACTLY the same as the original equation, then the graph is symmetric with respect to the x-axis.

7. The function could also be graphed to show that it is symmetric with respect to the x- axis.

8. Is the following equation symmetric with respect to the x-axis?

9. After substituting a –y for every y, the equation is EXACTLY the same as the original. Therefore, the equation is symmetric with respect to the x-axis.

10. The function could also be graphed to show that it is symmetric with respect to the x- axis.

11. Is the following equation symmetric with respect to the x-axis?

12. After substituting a –y for every y, the equation is NOT EXACTLY the same as the original. Therefore, the equation is NOT symmetric with respect to the x-axis.

13. Is the following equation symmetric with respect to the x-axis?

14. After substituting a –y for every y, the equation is NOT EXACTLY the same as the original. Therefore, the equation is NOT symmetric with respect to the x-axis.

15. The function could also be graphed to show that it is NOT symmetric with respect to the x- axis.

16. Is the following equation symmetric with respect to the x-axis?

17. After substituting a –y for every y, the equation is EXACTLY the same as the original. Therefore, the equation is symmetric with respect to the x-axis.

18. The function could also be graphed to show that it is symmetric with respect to the x- axis.

19. Congratulations!! You just completed symmetric with respect to the x-axis